# Quantum Superposition

## Main Question or Discussion Point

I need some help with a problem that involves the concept of quantum superposition. Suppose you have a nucleon cluster of matter helium-3 [PNP] and you attempt to combine with antimatter deuterons [N^P^], where ^ represents antimatter. Would it be possible that the two could form wavefunctions that allow for a quantum superposition rather than complete annihilation of the matter and antimatter quarks ? Thanks for any comments you can provide.

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Would the lack any of response to my initial post indicate that no current mathematical formalism exists in nuclear physics for possible superposition of a matter fermion cluster [PNP] with an antimatter boson cluster [N^P^] ?

CarlB
Homework Helper
Yeah, of course a superposition is possible. You're asking the Schroedinger's Cat question.

Carl

... and you attempt to combine with antimatter deuterons ...
can be translated as if you were preparing an experimental collision between the two systems. Right? Then, this means that the initial condition you consider is a superposition of the mixed states for the composite system. At the start the superposition is separable. But with evolution of this system all possible outcome will enter into the state vector of the system. However, if the collision is successful, some component -annihilation- may dominate the picture: annihilation is nearly certain. Conversely, if the collision is a little bit too much off-target the system will almost surely escape annihilation. This picture may be complemented by other possible outcomes ...

lalbatros said:
...if the collision is successful, some component -annihilation- may dominate the picture: annihilation is nearly certain. Conversely, if the collision is a little bit too much off-target the system will almost surely escape annihilation.
Thank you albatros. It is the second part of your above statement that I now try to understand from both the physics and more importantly the mathematics. Are you aware of any mathematical argument that would allow the collision to be successful, and for matter [PNP] + antimatter [N^P^] to form superposed union, and escape annihilation ? Perhaps some form of one of the Dirac equations ? If not, is there a mathematical argument that proves such collision as stated above impossible ? On first glance, one may think that collision of matter [PNP] + antimatter [N^P^], would just yield a [P], with the rest involved in annihilation and lots of gamma ray energy released. But, this would not happen if the two can form a superposition, this is what I try to understand mathematically, how such a superposition may be possible. Finally, has CERN or other experimental labs that work with antimatter ever tried this experiment ? It is really a very simple system to test, collision between matter helium-3 [PNP] with antimatter deuteron [N^P^], at different collision energies--does anyone know if this experiment has been conducted ?

David
Are you really interested in whether they can form a superposition or whether they can form a bound state? Matter and antimatter can form bound states, for example. See this article which talks about positronium. It's very short lived but can exist. It's not really clear from your question why exactly you are asking and knowing that would help us give you the information you need.